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Boussinesq, Schrödinger and Euler-Korteweg. (English) Zbl 07925344

Machihara, Shuji (ed.), Mathematical physics and its interactions. In honor of the 60th birthday of Tohru Ozawa, Tokyo, Japan, August 25–27, 2021. Conference proceedings. Singapore: Springer. Springer Proc. Math. Stat. 451, 255-282 (2024).

MSC: 35-XX

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Linares, Felipe; Mendez, Argenis J.; Pilod, Didier

Well-posedness for the extended Schrödinger-Benjamin-Ono system. (English) Zbl 07903086

Vietnam J. Math. 52, No. 4, 1043-1066 (2024).

MSC: 35Q55 35Q53 35A22 35B65 42A38 35A01 35A02

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Freire, Ricardo; Linares, Felipe; Muñoz, Claudio; Ponce, Gustavo

On local energy decay for solutions of the Benjamin-Ono equation. (English) Zbl 1539.35216

Ann. Inst. Henri Poincaré, Anal. Non Linéaire 41, No. 3, 725-747 (2024).

MSC: 35Q53 35Q51 37K10 37K15 35B40

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Killip, Rowan; Laurens, Thierry; Vişan, Monica

Sharp well-posedness for the Benjamin-Ono equation. (English) Zbl 1543.35207

Invent. Math. 236, No. 3, 999-1054 (2024).

Reviewer: Ti-Jun Xiao (Fudan)

MSC: 35Q53 35C08 37K35 42A38 35A01 35A02

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Moşincat, Răzvan; Pilod, Didier

Unconditional uniqueness for the Benjamin-Ono equation. (English) Zbl 1518.35012

Pure Appl. Anal. 5, No. 2, 285-322 (2023).

MSC: 35A02 35Q53 76B55

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Yang, Kai

High order conservative schemes for the generalized Benjamin-Ono equation on the unbounded domain. (English) Zbl 1530.35264

J. Sci. Comput. 96, No. 2, Paper No. 35, 27 p. (2023).

MSC: 35Q53 35L65 65M70 65M06 65L06 65N35 44A15

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Albarracin, Carolina; Rodriguez-Blanco, Guillermo

The IVP for a periodic generalized ZK equation. (English) Zbl 1508.35115

J. Differ. Equations 352, 1-22 (2023).

MSC: 35Q53 35A01 35A02 26A33 35R11 35B65

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Antonelli, Paolo; Marcati, Pierangelo; Scandone, Raffaele

Global well-posedness for the non-linear Maxwell-Schrödinger system. (English) Zbl 1498.35412

Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 23, No. 3, 1293-1324 (2022).

MSC: 35Q35 35Q40 35Q55 35Q60 76Y05 81V10 35B45

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Cunha, Alysson

On decay of the solutions for the dispersion generalized Benjamin-Ono and Benjamin-Ono equations. (English) Zbl 1496.35074

Adv. Differ. Equ. 27, No. 11-12, 781-822 (2022).

MSC: 35B40 35A02 35B60 35G25 35Q53 35R11

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Chen, Mingjuan; Guo, Boling; Han, Lijia

Uniform local well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation. (English) Zbl 1492.35252

Sci. China, Math. 65, No. 8, 1553-1576 (2022).

MSC: 35Q53 35Q55 35A01

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Kishimoto, Nobu

Unconditional uniqueness for the periodic Benjamin-Ono equation by normal form approach. (English) Zbl 1504.35337

J. Math. Anal. Appl. 514, No. 2, Article ID 126309, 22 p. (2022).

MSC: 35Q35 76B70 76B55 35A02 37K10

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Li, Jinlu; Yu, Yanghai; Zhu, Weipeng

Non-uniform dependence on initial data for the Benjamin-Ono equation. (English) Zbl 1504.35348

Nonlinear Anal., Real World Appl. 67, Article ID 103597, 10 p. (2022).

MSC: 35Q35 76B15 76B70 42B25 42A38

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Holmer, Justin; Zhang, Katherine Zhiyuan

Benjamin-Ono soliton dynamics in a slowly varying potential revisited. (English) Zbl 1537.35313

SIAM J. Math. Anal. 54, No. 2, 2634-2690 (2022).

MSC: 35Q53 35Q51 37K40 35C08 35A22 44A15

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Molinet, Luc; Tanaka, Tomoyuki

Unconditional well-posedness for some nonlinear periodic one-dimensional dispersive equations. (English) Zbl 1486.35004

J. Funct. Anal. 283, No. 1, Article ID 109490, 45 p. (2022).

MSC: 35A01 35A02 35Q53 35R11

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Freire, Ricardo. C.; Mendez, Argenis J.; Riaño, Oscar

On some regularity properties for the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov equation. (English) Zbl 1486.35099

J. Differ. Equations 322, 135-179 (2022).

MSC: 35B65 35G25 35S10

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de Moura, Roger P.; Nascimento, Ailton C.; Santos, Gleison N.

Local well-posedness for a fractional KdV-type equation. (English) Zbl 1486.35420

J. Evol. Equ. 22, No. 1, Paper No. 27, 26 p. (2022).

MSC: 35R11 35Q53

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Klein, Christian; Saut, Jean-Claude; Wang, Yuexun

On the modified fractional Korteweg-de Vries and related equations. (English) Zbl 1525.76021

Nonlinearity 35, No. 3, 1170-1212 (2022).

Reviewer: Denys Dutykh (Le Bourget-du-Lac)

MSC: 76B25 35Q53 26A33

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Roudenko, Svetlana; Wang, Zhongming; Yang, Kai

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study. (English) Zbl 07515841

J. Comput. Phys. 445, Article ID 110570, 25 p. (2021).

MSC: 35Qxx 76Bxx 65Mxx

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Isom, Bradley; Mantzavinos, Dionyssios; Oh, Seungly; Stefanov, Atanas

Polynomial bound and nonlinear smoothing for the Benjamin-Ono equation on the circle. (English) Zbl 1473.35486

J. Differ. Equations 297, 25-46 (2021).

MSC: 35Q53 35B65

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Chen, Mingjuan; Guo, Boling; Han, Lijia

Global well-posedness and inviscid limit for the generalized Benjamin-Ono-Burgers equation. (English) Zbl 1460.35312

Appl. Anal. 100, No. 4, 804-818 (2021).

MSC: 35Q53 35Q35 35A01 35A02 44A15 76B15

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Riaño, Oscar G.

Well-posedness for a two-dimensional dispersive model arising from capillary-gravity flows. (English) Zbl 1459.35318

J. Differ. Equations 280, 1-65 (2021).

MSC: 35Q35 76B15 76B45 35A01 35A02

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Tanaka, Tomoyuki

Local well-posedness for fourth order Benjamin-Ono type equations. (English) Zbl 1462.35312

J. Math. Anal. Appl. 498, No. 1, Article ID 124928, 33 p. (2021).

MSC: 35Q35 76B15 35A01 35A02

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Kita, Naoyasu; Wada, Takeshi

Sharp asymptotic behavior of solutions to Benjamin-Ono type equations – short range case. (English) Zbl 1459.35042

J. Math. Anal. Appl. 497, No. 2, Article ID 124879, 13 p. (2021).

MSC: 35B40 35G25 35R09

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Pilod, Didier; Saut, Jean-Claude; Selberg, Sigmund; Tesfahun, Achenef

Dispersive estimates for full dispersion KP equations. (English) Zbl 1458.35083

J. Math. Fluid Mech. 23, No. 1, Paper No. 25, 25 p. (2021).

MSC: 35B45 35Q35 35Q53 42B20

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Correia, Simão

Nonlinear smoothing and unconditional uniqueness for the Benjamin-Ono equation in weighted Sobolev spaces. (English) Zbl 1458.35325

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 205, Article ID 112227, 13 p. (2021).

MSC: 35Q35 35A02 35B65 42B37 44A15

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Nascimento, A. C.

On special regularity properties of solutions of the Benjamin-Ono-Zakharov-Kuznetsov (BO-ZK) equation. (English) Zbl 1460.35313

Commun. Pure Appl. Anal. 19, No. 9, 4285-4325 (2020).

MSC: 35Q53 35G31 35B65 35A01 35A02

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Mendez, Argenis J.

On the propagation of regularity for solutions of the dispersion generalized Benjamin-Ono equation. (English) Zbl 1462.35339

Anal. PDE 13, No. 8, 2399-2440 (2020).

MSC: 35Q53 35B65 35A01 35A02

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Zhang, Katherine Zhiyuan

Benjamin-Ono soliton dynamics in a slowly varying potential. (English) Zbl 1433.35349

Nonlinearity 33, No. 3, 1064-1093 (2020).

Reviewer: Ahmed Lesfari (El Jadida)

MSC: 35Q53 35Q51 37K40 35A30 44A15 35B20

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Kenig, C. E.; Ponce, G.; Vega, L.

Uniqueness properties of solutions to the Benjamin-Ono equation and related models. (English) Zbl 1433.35339

J. Funct. Anal. 278, No. 5, Article ID 108396, 14 p. (2020).

MSC: 35Q53 35B05 35Q35 76B15 35A02

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Saut, Jean-Claude

Benjamin-Ono and intermediate long wave equations: modeling, IST and PDE. (English) Zbl 1442.35355

Miller, Peter D. (ed.) et al., Nonlinear dispersive partial differential equations and inverse scattering. Papers from the focus program on “Nonlinear Dispersive Partial Differential Equations and Inverse Scattering”, Fields Institute, July 31 – August 18, 2017. New York, NY: Springer; Toronto, ON: The Fields Institute for Research in Mathematical Scienes. Fields Inst. Commun. 83, 95-160 (2019).

MSC: 35Q35 76B15 37K15

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Bustamante, Eddye; Jiménez Urrea, José; Mejía, Jorge

Periodic Cauchy problem for one two-dimensional generalization of the Benjamin-Ono equation in Sobolev spaces of low regularity. (English) Zbl 1427.35225

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 188, 50-69 (2019).

MSC: 35Q53 35B65 35A01 35A02 44A15

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Hickman, Jonathan; Linares, Felipe; Riaño, Oscar G.; Rogers, Keith M.; Wright, James

On a higher dimensional version of the Benjamin-Ono equation. (English) Zbl 1435.35300

SIAM J. Math. Anal. 51, No. 6, 4544-4569 (2019).

MSC: 35Q35 35B65 42B20 35R25 76B03

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Muñoz, Claudio; Ponce, Gustavo

On the asymptotic behavior of solutions to the Benjamin-Ono equation. (English) Zbl 1428.37069

Proc. Am. Math. Soc. 147, No. 12, 5303-5312 (2019).

MSC: 37K40 37K15 35Q53 35Q51 37K10

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Nascimento, A. C.

On the propagation of regularities in solutions of the fifth order Kadomtsev-Petviashvili II equation. (English) Zbl 1416.35085

J. Math. Anal. Appl. 478, No. 1, 156-181 (2019).

MSC: 35G25 35B65

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Linares, Felipe; Panthee, Mahendra; Robert, Tristan; Tzvetkov, Nikolay

On the periodic Zakharov-Kuznetsov equation. (English) Zbl 1420.35319

Discrete Contin. Dyn. Syst. 39, No. 6, 3521-3533 (2019).

MSC: 35Q53 35B05

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Bustamante, Eddye; Urrea, José Jiménez; Mejía, Jorge

The Cauchy problem for a family of two-dimensional fractional Benjamin-Ono equations. (English) Zbl 1411.35238

Commun. Pure Appl. Anal. 18, No. 3, 1177-1203 (2019).

MSC: 35Q53

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Molinet, Luc; Pilod, Didier; Vento, Stéphane

Unconditional uniqueness for the modified Korteweg-de Vries equation on the line. (English) Zbl 1410.35178

Rev. Mat. Iberoam. 34, No. 4, 1563-1608 (2018).

MSC: 35Q53 35A02 35E15 35B45 35B65 35D30

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Molinet, Luc; Pilod, Didier; Vento, Stéphane

On well-posedness for some dispersive perturbations of Burgers’ equation. (English) Zbl 1459.76024

Ann. Inst. Henri Poincaré, Anal. Non Linéaire 35, No. 7, 1719-1756 (2018).

MSC: 76B15 35Q35

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Flores, C.

Control and stability of the linearized dispersion-generalized Benjamin-Ono equation on a periodic domain. (English) Zbl 1401.93036

Math. Control Signals Syst. 30, No. 3, Paper No. 13, 16 p. (2018).

MSC: 93B05 93B17 93D15 35Q53 93C20

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Wu, Yilun

Jost solutions and the direct scattering problem of the Benjamin-Ono equation. (English) Zbl 1398.35140

SIAM J. Math. Anal. 49, No. 6, 5158-5206 (2017).

MSC: 35P25 35A22 35Q53

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Saut, Jean-Claude; Wang, Chao; Xu, Li

The Cauchy problem on large time for surface-waves-type Boussinesq systems. II. (English) Zbl 1412.35266

SIAM J. Math. Anal. 49, No. 4, 2321-2386 (2017).

Reviewer: Georg V. Jaiani (Tbilisi)

MSC: 35Q35 35A01 35Q53 76B03 76B15

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Ponce, Gustavo

On the IVP for the \(k\)-generalized Benjamin-Ono equation. (English) Zbl 1403.35087

Pereyra, María Cristina (ed.) et al., Harmonic analysis, partial differential equations, complex analysis, Banach spaces, and operator theory. Volume 1. Celebrating Cora Sadosky’s life. Cham: Springer (ISBN 978-3-319-30959-0/hbk; 978-3-319-30961-3/ebook). Association for Women in Mathematics Series 4, 349-371 (2016).

MSC: 35G61 35Q53

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Cunha, Alysson; Pastor, Ademir

The IVP for the Benjamin-Ono-Zakharov-Kuznetsov equation in low regularity Sobolev spaces. (English) Zbl 1338.35113

J. Differ. Equations 261, No. 3, 2041-2067 (2016).

MSC: 35G25

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Wu, Yilun

Simplicity and finiteness of discrete spectrum of the Benjamin-Ono scattering operator. (English) Zbl 1338.35321

SIAM J. Math. Anal. 48, No. 2, 1348-1367 (2016).

Reviewer: Petru A. Cojuhari (Kraków)

MSC: 35P25 47A40

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Isaza, Pedro; Linares, Felipe; Ponce, Gustavo

On the propagation of regularities in solutions of the Benjamin-Ono equation. (English) Zbl 1329.35268

J. Funct. Anal. 270, No. 3, 976-1000 (2016).

MSC: 35Q53 35B05

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Laurent, Camille; Linares, Felipe; Rosier, Lionel

Control and stabilization of the Benjamin-Ono equation in \(L^2(\mathbb T)\). (English) Zbl 1325.35166

Arch. Ration. Mech. Anal. 218, No. 3, 1531-1575 (2015).

MSC: 35Q35 35B35 93B05

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Linares, Felipe; Rosier, Lionel

Control and stabilization of the Benjamin-Ono equation on a periodic domain. (English) Zbl 1310.93031

Trans. Am. Math. Soc. 367, No. 7, 4595-4626 (2015).

MSC: 93B05 93D15 93D20 35Q53

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Kenig, Carlos E.; Pilod, Didier

Well-posedness for the fifth-order KdV equation in the energy space. (English) Zbl 1320.35313

Trans. Am. Math. Soc. 367, No. 4, 2551-2612 (2015).

Reviewer: Aleksey Kostenko (Donetsk)

MSC: 35Q53 35A01 35Q35 37K05 76B15

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Tzvetkov, Nikolay; Visciglia, Nicola

Invariant measures and long time behaviour for the Benjamin-Ono equation. II. (English. French summary) Zbl 1315.37051

J. Math. Pures Appl. (9) 103, No. 1, 102-141 (2015).

Reviewer: Andrew Pickering (Madrid)

MSC: 37L40 37K10

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Cunha, Alysson; Pastor, Ademir

The IVP for the Benjamin-Ono-Zakharov-Kuznetsov equation in weighted Sobolev spaces. (English) Zbl 1304.35606

J. Math. Anal. Appl. 417, No. 2, 660-693 (2014).

MSC: 35Q53

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Guo, Zihua; Lin, Yiquan; Molinet, Luc

Well-posedness in energy space for the periodic modified Benjamin-Ono equation. (English) Zbl 1315.35058

J. Differ. Equations 256, No. 8, 2778-2806 (2014).

Reviewer: David Ambrose (Philadelphia)

MSC: 35G31 35R09

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Fonseca, Germán; Linares, Felipe; Ponce, Gustavo

The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces. (English) Zbl 1511.35035

Ann. Inst. Henri Poincaré, Anal. Non Linéaire 30, No. 5, 763-790 (2013).

MSC: 35B40 35B60 35G25

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Flores, Cynthia

On decay properties of solutions to the IVP for the Benjamin-Ono equation. (English) Zbl 1290.35223

J. Dyn. Differ. Equations 25, No. 4, 907-923 (2013).

Reviewer: Ahmed Lesfari (El Jadida)

MSC: 35Q53 37K10

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Molinet, Luc; Wang, Yuzhao

Dispersive limit from the Kawahara to the KdV equation. (English) Zbl 1284.35378

J. Differ. Equations 255, No. 8, 2196-2219 (2013).

MSC: 35Q53

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Huh, Hyungjin

Energy solution to the Chern-Simons-Schrödinger equations. (English) Zbl 1276.35138

Abstr. Appl. Anal. 2013, Article ID 590653, 7 p. (2013).

MSC: 35Q60 35Q40

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Molinet, Luc; Pilod, Didier

Global well-posedness and limit behavior for a higher-order Benjamin-Ono equation. (English) Zbl 1258.35179

Commun. Partial Differ. Equations 37, No. 10-12, 2050-2080 (2012).

MSC: 35Q53 35A01 76B55

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Wada, Takeshi

Smoothing effects for Schrödinger equations with electro-magnetic potentials and applications to the Maxwell-Schrödinger equations. (English) Zbl 1251.35095

J. Funct. Anal. 263, No. 1, 1-24 (2012).

MSC: 35Q40 81Q05 35Q61

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Fonseca, Germán; Linares, Felipe; Ponce, Gustavo

The IVP for the Benjamin-Ono equation in weighted Sobolev spaces. II. (English) Zbl 1235.35243

J. Funct. Anal. 262, No. 5, 2031-2049 (2012).

MSC: 35Q53 35B60 46E35

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Esfahani, Amin

Remarks on solitary waves of the generalized two dimensional Benjamin-Ono equation. (English) Zbl 1236.45008

Appl. Math. Comput. 218, No. 2, 308-323 (2011).

Reviewer: Dan-Mircea Borş (Iaşi)

MSC: 45K05

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Guo, Zihua; Peng, Lizhong; Wang, Baoxiang; Wang, Yuzhao

Uniform well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation. (English) Zbl 1234.35072

Adv. Math. 228, No. 2, 647-677 (2011).

MSC: 35G25 35B25 35Q53

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Linares, Felipe; Pilod, Didier; Ponce, Gustavo

Well-posedness for a higher-order Benjamin-Ono equation. (English) Zbl 1205.35261

J. Differ. Equations 250, No. 1, 450-475 (2011).

MSC: 35Q53 76B15 35B45 35A01 35A02 35A30

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Fonseca, Germán; Ponce, Gustavo

The IVP for the Benjamin-Ono equation in weighted Sobolev spaces. (English) Zbl 1205.35249

J. Funct. Anal. 260, No. 2, 436-459 (2011).

MSC: 35Q53 35B60 46E35

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Cui, Shangbin; Kenig, Carlos E.

Weak continuity of the flow map for the Benjamin-Ono equation on the line. (English) Zbl 1223.35272

J. Fourier Anal. Appl. 16, No. 6, 1021-1052 (2010).

Reviewer: Mats Ehrnström (Hannover)

MSC: 35Q53 35B30

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Esfahani, Amin; Pastor, Ademir

Instability of solitary wave solutions for the generalized BO-ZK equation. (English) Zbl 1181.35232

J. Differ. Equations 247, No. 12, 3181-3201 (2009).

MSC: 35Q53 35Q35 35B35 35Q51 35B45 35C08

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Kwon, Soonsik

On the fifth-order KdV equation: Local well-posedness and lack of uniform continuity of the solution map. (English) Zbl 1153.35067

J. Differ. Equations 245, No. 9, 2627-2659 (2008).

MSC: 35Q53 37K10 35B45

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Burq, Nicolas; Planchon, Fabrice

On well-posedness for the Benjamin-Ono equation. (English) Zbl 1148.35074

Math. Ann. 340, No. 3, 497-542 (2008).

Reviewer: Grzegorz Karch (Wrocław)

MSC: 35Q53 35A05 76B03

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Nakamura, Makoto; Wada, Takeshi

Global existence and uniqueness of solutions to the Maxwell-Schrödinger equations. (English) Zbl 1134.81020

Commun. Math. Phys. 276, No. 2, 315-339 (2007).

MSC: 81Q05 35Q40 35Q60 81V10

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Molinet, L.; Saut, J. C.; Tzvetkov, N.

Global well-posedness for the KP-I equation on the background of a non-localized solution. (English) Zbl 1160.35065

Commun. Math. Phys. 272, No. 3, 775-810 (2007).

Reviewer: Q. P. Liu (Beijing)

MSC: 35Q53 35B30

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Ionescu, Alexandru D.; Kenig, Carlos E.

Global well-posedness of the Benjamin–Ono equation in low-regularity spaces. (English) Zbl 1123.35055

J. Am. Math. Soc. 20, No. 3, 753-798 (2007).

Reviewer: Boris V. Loginov (Ul’yanovsk)

MSC: 35Q53 35Q05

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Molinet, Luc

Global well-posedness in the energy space for the Benjamin-Ono equation on the circle. (English) Zbl 1140.35001

Math. Ann. 337, No. 2, 353-383 (2007).

MSC: 35A05 45K05

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Otani, Masanori

Well-posedness of the generalized Benjamin-Ono-Burgers equations in Sobolev spaces of negative order. (English) Zbl 1145.35305

Osaka J. Math. 43, No. 4, 935-965 (2006).

MSC: 35A07 35G10 35Q53 76B15

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Kim, Jong Uhn

On the stochastic Benjamin–Ono equation. (English) Zbl 1107.35105

J. Differ. Equations 228, No. 2, 737-768 (2006).

Reviewer: Aleksandr D. Borisenko (Kyïv)

MSC: 35R60 60H15

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Kita, Naoyasu; Segata, Jun-ichi

Time local well-posedness for the Benjamin-Ono equation with large initial data. (English) Zbl 1101.35067

Publ. Res. Inst. Math. Sci. 42, No. 1, 143-171 (2006).

MSC: 35Q53 76B55 35A07

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Linares, Felipe; Ortega, Jaime H.

On the controllability and stabilization of the linearized Benjamin-Ono equation. (English) Zbl 1125.93006

ESAIM, Control Optim. Calc. Var. 11, 204-218 (2005).

MSC: 93B05 35B37 35Q53 76B75 93C20 93D15

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Huo, Zhaohui; Guo, Boling

The Cauchy problem for the generalized Korteweg-de Vries-Benjamin-Ono equation with low regularity data. (English) Zbl 1088.35059

Acta Math. Sin., Engl. Ser. 21, No. 5, 1191-1196 (2005).

MSC: 35Q53 35A07 35E15 35G25 37K10

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Kenig, Carlos E.

On the local and global well-posedness theory for the KP-I equation. (English) Zbl 1072.35162

Ann. Inst. Henri Poincaré, Anal. Non Linéaire 21, No. 6, 827-838 (2004).

Reviewer: Boris V. Loginov (Ul’yanovsk)

MSC: 35Q53 76B45 35B30 76B03

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Found 76 Documents (Results 1–76)

Boussinesq, Schrödinger and Euler-Korteweg. (English) Zbl 07925344

Well-posedness for the extended Schrödinger-Benjamin-Ono system. (English) Zbl 07903086

On local energy decay for solutions of the Benjamin-Ono equation. (English) Zbl 1539.35216

Sharp well-posedness for the Benjamin-Ono equation. (English) Zbl 1543.35207

Unconditional uniqueness for the Benjamin-Ono equation. (English) Zbl 1518.35012

High order conservative schemes for the generalized Benjamin-Ono equation on the unbounded domain. (English) Zbl 1530.35264

The IVP for a periodic generalized ZK equation. (English) Zbl 1508.35115

Global well-posedness for the non-linear Maxwell-Schrödinger system. (English) Zbl 1498.35412

On decay of the solutions for the dispersion generalized Benjamin-Ono and Benjamin-Ono equations. (English) Zbl 1496.35074

Uniform local well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation. (English) Zbl 1492.35252

Unconditional uniqueness for the periodic Benjamin-Ono equation by normal form approach. (English) Zbl 1504.35337

Non-uniform dependence on initial data for the Benjamin-Ono equation. (English) Zbl 1504.35348

Benjamin-Ono soliton dynamics in a slowly varying potential revisited. (English) Zbl 1537.35313

Unconditional well-posedness for some nonlinear periodic one-dimensional dispersive equations. (English) Zbl 1486.35004

On some regularity properties for the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov equation. (English) Zbl 1486.35099

Local well-posedness for a fractional KdV-type equation. (English) Zbl 1486.35420

On the modified fractional Korteweg-de Vries and related equations. (English) Zbl 1525.76021

Dynamics of solutions in the generalized Benjamin-Ono equation: a numerical study. (English) Zbl 07515841

Polynomial bound and nonlinear smoothing for the Benjamin-Ono equation on the circle. (English) Zbl 1473.35486

Global well-posedness and inviscid limit for the generalized Benjamin-Ono-Burgers equation. (English) Zbl 1460.35312

Well-posedness for a two-dimensional dispersive model arising from capillary-gravity flows. (English) Zbl 1459.35318

Local well-posedness for fourth order Benjamin-Ono type equations. (English) Zbl 1462.35312

Sharp asymptotic behavior of solutions to Benjamin-Ono type equations – short range case. (English) Zbl 1459.35042

Dispersive estimates for full dispersion KP equations. (English) Zbl 1458.35083

Nonlinear smoothing and unconditional uniqueness for the Benjamin-Ono equation in weighted Sobolev spaces. (English) Zbl 1458.35325

On special regularity properties of solutions of the Benjamin-Ono-Zakharov-Kuznetsov (BO-ZK) equation. (English) Zbl 1460.35313

On the propagation of regularity for solutions of the dispersion generalized Benjamin-Ono equation. (English) Zbl 1462.35339

Benjamin-Ono soliton dynamics in a slowly varying potential. (English) Zbl 1433.35349

Uniqueness properties of solutions to the Benjamin-Ono equation and related models. (English) Zbl 1433.35339

Benjamin-Ono and intermediate long wave equations: modeling, IST and PDE. (English) Zbl 1442.35355

Periodic Cauchy problem for one two-dimensional generalization of the Benjamin-Ono equation in Sobolev spaces of low regularity. (English) Zbl 1427.35225

On a higher dimensional version of the Benjamin-Ono equation. (English) Zbl 1435.35300

On the asymptotic behavior of solutions to the Benjamin-Ono equation. (English) Zbl 1428.37069

On the propagation of regularities in solutions of the fifth order Kadomtsev-Petviashvili II equation. (English) Zbl 1416.35085

On the periodic Zakharov-Kuznetsov equation. (English) Zbl 1420.35319

The Cauchy problem for a family of two-dimensional fractional Benjamin-Ono equations. (English) Zbl 1411.35238

Unconditional uniqueness for the modified Korteweg-de Vries equation on the line. (English) Zbl 1410.35178

On well-posedness for some dispersive perturbations of Burgers’ equation. (English) Zbl 1459.76024

Control and stability of the linearized dispersion-generalized Benjamin-Ono equation on a periodic domain. (English) Zbl 1401.93036

Jost solutions and the direct scattering problem of the Benjamin-Ono equation. (English) Zbl 1398.35140

The Cauchy problem on large time for surface-waves-type Boussinesq systems. II. (English) Zbl 1412.35266

On the IVP for the \(k\)-generalized Benjamin-Ono equation. (English) Zbl 1403.35087

The IVP for the Benjamin-Ono-Zakharov-Kuznetsov equation in low regularity Sobolev spaces. (English) Zbl 1338.35113

Simplicity and finiteness of discrete spectrum of the Benjamin-Ono scattering operator. (English) Zbl 1338.35321

On the propagation of regularities in solutions of the Benjamin-Ono equation. (English) Zbl 1329.35268

Control and stabilization of the Benjamin-Ono equation in \(L^2(\mathbb T)\). (English) Zbl 1325.35166

Control and stabilization of the Benjamin-Ono equation on a periodic domain. (English) Zbl 1310.93031

Well-posedness for the fifth-order KdV equation in the energy space. (English) Zbl 1320.35313

Invariant measures and long time behaviour for the Benjamin-Ono equation. II. (English. French summary) Zbl 1315.37051

The IVP for the Benjamin-Ono-Zakharov-Kuznetsov equation in weighted Sobolev spaces. (English) Zbl 1304.35606

Well-posedness in energy space for the periodic modified Benjamin-Ono equation. (English) Zbl 1315.35058

The IVP for the dispersion generalized Benjamin-Ono equation in weighted Sobolev spaces. (English) Zbl 1511.35035

On decay properties of solutions to the IVP for the Benjamin-Ono equation. (English) Zbl 1290.35223

Dispersive limit from the Kawahara to the KdV equation. (English) Zbl 1284.35378

Energy solution to the Chern-Simons-Schrödinger equations. (English) Zbl 1276.35138

Global well-posedness and limit behavior for a higher-order Benjamin-Ono equation. (English) Zbl 1258.35179

Smoothing effects for Schrödinger equations with electro-magnetic potentials and applications to the Maxwell-Schrödinger equations. (English) Zbl 1251.35095

The IVP for the Benjamin-Ono equation in weighted Sobolev spaces. II. (English) Zbl 1235.35243

Remarks on solitary waves of the generalized two dimensional Benjamin-Ono equation. (English) Zbl 1236.45008

Uniform well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation. (English) Zbl 1234.35072

Well-posedness for a higher-order Benjamin-Ono equation. (English) Zbl 1205.35261

The IVP for the Benjamin-Ono equation in weighted Sobolev spaces. (English) Zbl 1205.35249

Weak continuity of the flow map for the Benjamin-Ono equation on the line. (English) Zbl 1223.35272

Instability of solitary wave solutions for the generalized BO-ZK equation. (English) Zbl 1181.35232

On the fifth-order KdV equation: Local well-posedness and lack of uniform continuity of the solution map. (English) Zbl 1153.35067

On well-posedness for the Benjamin-Ono equation. (English) Zbl 1148.35074

Global existence and uniqueness of solutions to the Maxwell-Schrödinger equations. (English) Zbl 1134.81020

Global well-posedness for the KP-I equation on the background of a non-localized solution. (English) Zbl 1160.35065

Global well-posedness of the Benjamin–Ono equation in low-regularity spaces. (English) Zbl 1123.35055

Global well-posedness in the energy space for the Benjamin-Ono equation on the circle. (English) Zbl 1140.35001

Well-posedness of the generalized Benjamin-Ono-Burgers equations in Sobolev spaces of negative order. (English) Zbl 1145.35305

On the stochastic Benjamin–Ono equation. (English) Zbl 1107.35105

Time local well-posedness for the Benjamin-Ono equation with large initial data. (English) Zbl 1101.35067

On the controllability and stabilization of the linearized Benjamin-Ono equation. (English) Zbl 1125.93006